1. Field of the Invention
The present invention relates to a rising and moving apparatus that is capable of rising and moving by flapping motion of wings, and to a method of manufacturing the same.
2. Description of the Background Art
Recently, studies have been made vigorously to realize technical implementation of flapping flight that is superior in maneuverability to ordinary flight of a conventional airplane. This largely depends on development in methods of analysis in the field of unsteady aerodynamics. Further, it has become possible, by using an enlarged scale model measuring technique, to analyze behavior of a fluid caused by a very quick motion such as flapping motion of an insect, as the motion of a frequency as high as several tens Hz to 1 kHz can be replaced by a motion of a frequency as low as several mHz. This much contributes to the methods of analysis in the field of unsteady aerodynamics.
In an article entitled “Wing Rotation and the Aerodynamic Basis of Insect Flight” (SCIENCE 1999 June VOL 284 pp. 1954–1960), M. Dickinson et al. reported the following experiment.
M. Dickinson et al. first prepared an enlarged scale model of wings of a fly. Then, in a fluid including floating particles, the enlarged scale model of the fly wings was moved in a flapping motion similar to the flapping motion of the fly. Here, the flapping motion similar to the flapping motion of the fly refers to a motion represented by a graph time-sequentially representing the flapping motion of the fly with only the time axis enlarged or reduced.
From the observation of the motion, particle motion when the enlarged scale model was flapped in the fluid is extracted as images. Further, by a force sensor provided at a root of the wing, a lift force was measured. Here, the Reynolds number in a situation that the enlarged scale model flaps in the fluid is equivalent to the Reynolds number in a situation that the fly flaps in the air. From the measurements of the enlarged scale model flapping in the fluid, the behavior of the air and the stress exerted by the air on the wings of the fly when the fly conduct a flapping flight and flies were clarified.
The article mentioned above describes that, as a result of analysis of interaction between the fluid and the structure at the time of hovering, at which it is most difficult to attain lift force, it was clarified that three principles related to generation of lift force, that is, 1. delayed stall, 2. rotational lift and 3. wake capture were to be well utilized in flapping flight, as will be described in the following.
1: Delayed Stall
A vortex referred to as a leading edge vortex generates around the wing of an ordinary airplane. The leading edge vortex may sometimes be separated from the wing, possibly resulting in a stall. In the flapping flight of a fly, the wings are moved reciprocally forward and backward, and the wing stroke is reversed before occurrence of a stall in the reciprocal motion. Therefore, it is possible to prevent the stall of the wing resulting from the leading edge vortex. Further, in the flapping flight of the fly, the lift force can be increased by utilizing the leading edge vortex.
2: Rotational Lift
The directions of motion of the wing before and after the stroke reversal of the flapping motion are opposite to each other. Therefore, immediately before and immediately after the stroke reversal, the velocity of motion of the wing decreases considerably. At this time, the wing rotates (is twisted) about an axis that extends along the longitudinal direction (direction of the wing span) as the central axis of rotation and makes a translational motion (motion in the forward/backward direction). Thus, the absolute velocity of the fluid flowing above the wing along the surface of the wing becomes larger than that of the fluid flowing below the wing along the surface of the wing.
Therefore, the pressure exerted from above to the wing surface becomes lower than the pressure exerted from below to the wing surface. As a result, a lift force acts on the wing. The lift force is referred to as rotational lift. The rotational lift compensates for the decrease in velocity of the wing immediately before and immediately after the stroke reversal in the flapping motion. Even when the direction of motion in the forward/backward direction of the wing is reversed by the twist of the wing in timing of the stroke reversal, the angle of attack of the wing can assume an appropriate angle with respect to the flow of the fluid.
3: Wake Capture
After the stroke reversal of the wing in the flapping motion, the flow of the fluid that is generated by the flapping motion before the reversal, that is, the wake, collides against the wing surface at a prescribed angle of attack. Specifically, after the stroke reversal, the wing collides against the fluid flowing in a direction opposite to the direction of motion of the wing. Accordingly, the wing after stroke reversal can obtain the lift force that is equivalent to the lift force generated when the wing is moved at a velocity equal to the sum of the velocity of motion of the wing and the velocity of the wake mentioned above. The collision of the wake and the wing surface as such is referred to as wake capture. The wake capture compensates for the decrease in lift force before and after the stroke reversal in the flapping motion.
The authors of the article above propose a method of obtaining an almost uniform lift force in flapping flight, utilizing the three mechanisms for generating the lift force described above.
In the study by M. Dickinson et al., interaction between the fluid and the structure is analyzed, assuming that the wing is a rigid body that does not substantially deform. The wing as a rigid body, however, has an aerodynamically adverse effect on the flapping flight of the rising and moving apparatus. This will be specifically described in the following.
In the following, “fluid velocity” means the relative velocity of the fluid between the wing and the fluid, unless specified otherwise. Namely, the fluid velocity refers to the relative fluid velocity. In this respect, the velocity of the fluid with respect to a coordinate system fixed in the space will be referred to as an absolute velocity.
1: Decrease in Efficiency in Utilizing the Delayed Stall when a Wing as a Rigid Body is Used.
The wing makes a rotational motion about the root of the wing as a center. Thus, the velocity of motion at the root of the wing is different from the velocity of motion at the tip end of the wing. Generally, when the angle of attack is constant, the velocity at which stall occurs is also constant. Further, the angle of attack is constant over the entire region of the wing, if the wing is flat.
Therefore, when the delayed stall is to be effectively utilized at the tip end portion of the wing, the delayed stall cannot be effectively utilized at the root of the wing. It may be possible to change the angle of attack portion by portion of the wing, in order to effectively utilize the delayed stall at the root of the wing. The wing having different angles of attack portion by portion, however, is suitable for a motion in one direction of progress of the forward/backward reciprocal motion of the wing but not at all suitable for a motion in the other direction of the forward/backward reciprocal motion of the wing.
2: Instability of Flapping Motion Caused by Reaction Generated at the Wing when Wing as a Rigid Body is Used
In the flapping motion, it is necessary to attain a lift force for supporting the weight of the rising and moving apparatus itself. Therefore, a force approximately the same or larger than the weight of itself acts on the wing. According to the article mentioned above, as the direction of motion of the wing changes and the angle of attack of the wing with respect to the fluid changes, the direction of the force exerted on the wing changes from the vertical direction to the horizontal direction.
Further, the force exerted to the wing as a rigid body is directly propagated from the driving unit to the wing. Therefore, the phase of the force applied to the wing is the same as the phase of the force applied to the driving unit. As a result, the rising and moving apparatus has its attitude or position changed considerably, because of the reaction of the force exerted on the wing.
At this time, the driving unit (actuator) must realize such a manner of flapping that compensates for the change in attitude of the rising and moving apparatus. Further, as the attitude of the rising and moving apparatus changes, the behavior of the fluid changes. Accordingly, it may also be necessary to change the manner of flapping itself. This makes the state of rising more instable, and the manner of flight would be complicated.
In order to solve the above described problems, a control unit is necessary that can exactly detect the change in attitude of the rising and moving apparatus caused in association with the flapping motion and that can perform high-speed information processing for calculating the new manner of flapping of the wing reflecting the change in attitude of the driving unit.
3: Increase in Mass and Cost of the Wing Resulting from the use of the Wing as a Rigid Body
Even when the adverse effects associated with the problems above are negligible, it is necessary to increase the thickness of the wing or to use a material having a very high stiffness for the wing, in order to manufacture a wing that is not much deformed by the flapping motion. This poses a new problem that the mass or the manufacturing cost of the wing increases.
On the contrary, when the wing is too soft, the following problems arise.
1: Decrease of Lift Force Caused by Decreased Angle of Attack
When the wing is too soft, the wing excessively turns aside the fluid that collides against the wing, and hence, the lift force generated at the wing decreases.
2: Decrease of Efficiency in Generating Rotational Lift
In order to generate rotational lift, it is necessary to generate a large difference between the absolute velocity of the fluid flowing above the wing along the wing surface and the absolute velocity of the fluid flowing below the wing along the wing surface. The wing having low stiffness, however, is easily deformed by the flow of the fluid. Therefore, when the wing having a low stiffness is used, the difference between the absolute velocity above the wing and the absolute velocity below the wing mentioned above becomes small. Accordingly, when the wing has a low stiffness, the rotational force of the wing decreases as compared with the wing having a high stiffness.
3: Timing Mismatch Among Motions of Various Portions of the Wing in Wake Capture
Wake capture occurs when the direction of translational motion of the wing is reversed. When the stiffness of the wing is excessively low, the amount of deformation of the wing becomes large. Thus, the timing of motion at the tip end of the wing lags behind the timing of motion of the root portion of the wing. Because of this timing delay, the timing of wake capture at the tip end portion of the wing lags behind the timing of wake capture at the root of the wing. Consequently, when the stiffness of the wing is too low, the efficiency of wake capture lowers.
The considerations above lead to the following.
There is an optimal value of stiffness of the wing. Therefore, different from the conventional example in which the wing is assumed to be a rigid body, it is necessary to analyze the manner of motion of the wing assuming that the wing passively deforms because of the fluid force. For the analysis including the interaction of the fluid and the structure using a wing that passively deforms, a technique of estimating stiffness of the wing suitable for flapping flight becomes necessary. The dynamical equivalent model of M. Dickinson et al. above, however, does not establish the technique.
The study discussed above is based on a principle that when two states are compared that structures which are similar are placed in different types of fluids and the Reynolds numbers of these two state are the same, behaviors of the fluids generated in these two states are similar. It is noted, however, that the governing rule of a structure such as a wing and the governing rule of a fluid such as the air differ, and hence the principle described above that governs the behavior of the fluid does not apply to the structure such as the wing.
By way of example, let us consider a corrugated plate or a wave plate used as a member of the wing. It is assumed that the plate has a tetragonal shape.
First, it is assumed that the wave plate is cantilevered, with a prescribed cross section along the direction orthogonal to the extension of ridges or valleys being a fixed end. Namely, the wave plate is assumed to be a cantilever extending in a direction parallel the direction of extension of the ridges or valleys. When there is an equally distributed vertical load on one side of the wave plate constituting the free end of the assumed cantilever, the amount of displacement of the free end of the cantilever is in inverse proportion to the thickness of the wave plate.
In contrast, assume that the wave plate is cantilevered with a prescribed cross section along the direction parallel to the direction of extension of the ridges of valleys being a fixed end. Namely, the wave plate is a cantilever extending in a direction orthogonal to the direction of extension of ridges or valleys. When there is an equally distributed vertical load on one side of the wave plate constituting the free end of the assumed cantilever, the amount of displacement of the free end of the cantilever is in inverse proportion to the cube of the thickness of the wave plate.
From the assumptions above, it is understood that even a structure having a very simple shape such as a wave plate has different stiffness to resist fluid force dependent on the manner how the fluid force acts on the structure. Therefore, it is not possible, by simply considering the manner of deformation of the wing when a fluid force is exerted on the wing in one prescribed manner, to determine the stiffness of every portion of the wing. Thus, it is difficult to produce an enlarged scale model of a wing that is similar to the wing of an actual insect and deforms in a manner similar to that of the actual wing of the insect.
When the enlarged scale model of the wing of an insect is not used, it is necessary to measure fluid flow behavior that is smaller than the order of mm (millimeter), while a wing model of the same size as the actual wing of the insect is in motion at a frequency as high as several tens Hz or higher. It is difficult, however, to form a wing model that is smaller than the mm order and experiences deformation similar to that of the wing of an insect, and to form a mechanism that drives such a wing model. Further, a sensor for measuring the lift force and pressure distribution on the wing model has the size of about a few millimeters, and the presence of the sensor itself causes variations in the behavior of the fluid. Thus, exact measurement of the fluid behavior is practically impossible by the method described above.
Numerical calculation employed for designing airplanes is also based on a precondition that the wing is a rigid body. There has been no method of calculation that can handle passive deformation of the wing.
In short, the wing as a rigid body that has been conventionally used for analyzing the behavior of the wing is not suitable for flapping flight as compared with a wing having an appropriate softness. Conventional studies of rising and moving apparatuses have not provided any method of manufacturing the wing having an appropriate softness for the flapping flight.